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igraph is a huge R library. Igraph is available as R, python and C library.
igraph. This course is not intended as an igraph course.

In R, igraph is installed in the usual way, i. e.

install.packages(“igraph”)

library(igraph)
## 
## Attaching package: 'igraph'
## The following objects are masked from 'package:stats':
## 
##     decompose, spectrum
## The following object is masked from 'package:base':
## 
##     union

An empty graph/network with five spherical yellow vertex is created by

g <- make_empty_graph(n=5, directed=TRUE)
#V(g) means Vertex(g)
V(g)$color = "yellow"
V(g)$shape = "sphere"

The command for visualizing a network is the function plot()

plot(g)

Add the next edges to the network 1->2, 1->3, 2->4, 3->4, 4->5.

g <- add.edges(g, c(1,2, 1,3, 2,4, 3,4, 4,5))
plot(g)

Add a red spherical vertex and add up to the network the next edges : 3->6, 6->5.

g <- add.vertices(g, 1, color="red", shape="sphere")
plot(g)

g <- add.edges(g, c(3,6, 6,5))
plot(g)

The class (vector, matrix,data.frame, network, etc) of an object in R is obtained using the command class(object). Igraph provides its own class (“igraph”)

class(g)
## [1] "igraph"

The structure of an object in R is obtained using the function str(object).

Replace connection 1-> 3 with connection 3-> 1.

g <- delete.edges(g, c(2))
g <- add.edges(g, c(3,1))

Name the nodes consecutively with the letters A-F.

V(g)$name <- LETTERS[1:6]
V(g)
## + 6/6 vertices, named, from 8732b2a:
## [1] A B C D E F
E(g)
## + 7/7 edges from 8732b2a (vertex names):
## [1] A->B B->D C->D D->E C->F F->E C->A

1 Degree

The command for the degree is the function degree(igraph_object)

degree(g)
## A B C D E F 
## 2 2 3 3 2 2

Plot the network in such way that that size of the nodes is propotional to the number of input connections

plot(g, layout=layout_nicely, vertex.size=degree(g, V(g), "in")*15+15,
     vertex.label.dist=0.5, edge.arrow.size=0.5)

Find and plot the degree distribution

plot(degree_distribution(g), main="Degree distribution", xlab="Degree", ylab="Frequency")

hist(degree(g),col="salmon")

The adjacency matrix is obtained by get.adjacency(igraph_object)

adj_mat<-as.matrix(get.adjacency(g))
adj_mat
##   A B C D E F
## A 0 1 0 0 0 0
## B 0 0 0 1 0 0
## C 1 0 0 1 0 1
## D 0 0 0 0 1 0
## E 0 0 0 0 0 0
## F 0 0 0 0 1 0

Plot a heat map from this matrix

heatmap(adj_mat, Rowv=NA, Colv="Rowv")

Some special networks are available in igraph

Try to figure out what kind networks generate the previous commands before running them!

1.1 Data sets: edgelist

The first data set we are going to work with consists of two files, “Dataset1-Media-Example-NODES.csv” and “Dataset1-Media-Example-EDGES.csv” Download here .

complete_address<-"~/Dropbox/BioInfo2017/polnet2018/Data files/"
nodes <- read.csv(paste0(complete_address,"Dataset1-Media-Example-NODES.csv"), header=T, as.is=T)
links <- read.csv(paste0(complete_address,"Dataset1-Media-Example-EDGES.csv"), header=T, as.is=T)

Examine the data

head(nodes)
id media media.type type.label audience.size
s01 NY Times 1 Newspaper 20
s02 Washington Post 1 Newspaper 25
s03 Wall Street Journal 1 Newspaper 30
s04 USA Today 1 Newspaper 32
s05 LA Times 1 Newspaper 20
s06 New York Post 1 Newspaper 50 
head(links)
from to type weight
s01 s02 hyperlink 22
s01 s03 hyperlink 22
s01 s04 hyperlink 21
s01 s15 mention 20
s02 s01 hyperlink 23
s02 s03 hyperlink 21

or using View(object)

View(nodes)
View(links)

1.2 Creating an igraph object

Next we will convert the raw data to an igraph network object. To do that, we will use the graph_from_data_frame() function, which requires two data frames: nodes and vertices. nodes: describes the edges of the network. Its first two columns are the IDs of the source and the target node for each edge. links: describes the vertices which starts with a column of node IDs. Any following columns are interpreted as node attributes. This parameter can be omitted - in that case the igraph object will be generated based solely on the link structure in nodes.

net <- graph_from_data_frame(d=links, vertices=nodes, directed=T) 
net
## IGRAPH 1bea8a1 DNW- 17 49 -- 
## + attr: name (v/c), media (v/c), media.type (v/n), type.label
## | (v/c), audience.size (v/n), type (e/c), weight (e/n)
## + edges from 1bea8a1 (vertex names):
##  [1] s01->s02 s01->s03 s01->s04 s01->s15 s02->s01 s02->s03 s02->s09
##  [8] s02->s10 s03->s01 s03->s04 s03->s05 s03->s08 s03->s10 s03->s11
## [15] s03->s12 s04->s03 s04->s06 s04->s11 s04->s12 s04->s17 s05->s01
## [22] s05->s02 s05->s09 s05->s15 s06->s06 s06->s16 s06->s17 s07->s03
## [29] s07->s08 s07->s10 s07->s14 s08->s03 s08->s07 s08->s09 s09->s10
## [36] s10->s03 s12->s06 s12->s13 s12->s14 s13->s12 s13->s17 s14->s11
## [43] s14->s13 s15->s01 s15->s04 s15->s06 s16->s06 s16->s17 s17->s04

The description of an igraph object starts with four letters:

D or U, for a directed or undirected graph
N for a named graph (where nodes have a name attribute)
W for a weighted graph (where edges have a weight attribute)
B for a bipartite (two-mode) graph (where nodes have a type attribute)

The two numbers that follow (17 49) refer to the number of nodes and edges in the graph. The description also lists node & edge attributes, for example:

(g/c) - graph-level character attribute
(v/c) - vertex-level character attribute
(e/n) - edge-level numeric attribute

We also have easy access to nodes, edges, and their attributes with:

E(net)       # The edges of the "net" object
## + 49/49 edges from 1bea8a1 (vertex names):
##  [1] s01->s02 s01->s03 s01->s04 s01->s15 s02->s01 s02->s03 s02->s09
##  [8] s02->s10 s03->s01 s03->s04 s03->s05 s03->s08 s03->s10 s03->s11
## [15] s03->s12 s04->s03 s04->s06 s04->s11 s04->s12 s04->s17 s05->s01
## [22] s05->s02 s05->s09 s05->s15 s06->s06 s06->s16 s06->s17 s07->s03
## [29] s07->s08 s07->s10 s07->s14 s08->s03 s08->s07 s08->s09 s09->s10
## [36] s10->s03 s12->s06 s12->s13 s12->s14 s13->s12 s13->s17 s14->s11
## [43] s14->s13 s15->s01 s15->s04 s15->s06 s16->s06 s16->s17 s17->s04
V(net)       # The vertices of the "net" object
## + 17/17 vertices, named, from 1bea8a1:
##  [1] s01 s02 s03 s04 s05 s06 s07 s08 s09 s10 s11 s12 s13 s14 s15 s16 s17
E(net)$type  # Edge attribute "type"
##  [1] "hyperlink" "hyperlink" "hyperlink" "mention"   "hyperlink"
##  [6] "hyperlink" "hyperlink" "hyperlink" "hyperlink" "hyperlink"
## [11] "hyperlink" "hyperlink" "mention"   "hyperlink" "hyperlink"
## [16] "hyperlink" "mention"   "mention"   "hyperlink" "mention"  
## [21] "mention"   "hyperlink" "hyperlink" "mention"   "hyperlink"
## [26] "hyperlink" "mention"   "mention"   "mention"   "hyperlink"
## [31] "mention"   "hyperlink" "mention"   "mention"   "mention"  
## [36] "hyperlink" "mention"   "hyperlink" "mention"   "hyperlink"
## [41] "mention"   "mention"   "mention"   "hyperlink" "hyperlink"
## [46] "hyperlink" "hyperlink" "mention"   "hyperlink"
V(net)$media # Vertex attribute "media"
##  [1] "NY Times"            "Washington Post"     "Wall Street Journal"
##  [4] "USA Today"           "LA Times"            "New York Post"      
##  [7] "CNN"                 "MSNBC"               "FOX News"           
## [10] "ABC"                 "BBC"                 "Yahoo News"         
## [13] "Google News"         "Reuters.com"         "NYTimes.com"        
## [16] "WashingtonPost.com"  "AOL.com"
# Find nodes and edges by attribute:
# (that returns oblects of type vertex sequence/edge sequence)
V(net)[media=="BBC"]
## + 1/17 vertex, named, from 1bea8a1:
## [1] s11
E(net)[type=="mention"]
## + 20/49 edges from 1bea8a1 (vertex names):
##  [1] s01->s15 s03->s10 s04->s06 s04->s11 s04->s17 s05->s01 s05->s15
##  [8] s06->s17 s07->s03 s07->s08 s07->s14 s08->s07 s08->s09 s09->s10
## [15] s12->s06 s12->s14 s13->s17 s14->s11 s14->s13 s16->s17
# You can also accesss the network matrix directly:
net[1,]
## s01 s02 s03 s04 s05 s06 s07 s08 s09 s10 s11 s12 s13 s14 s15 s16 s17 
##   0  22  22  21   0   0   0   0   0   0   0   0   0   0  20   0   0
net[5,7]
## [1] 0

It is also easy to extract an edge list or matrix back from the igraph network:

# Get an edge list or a matrix:
as_edgelist(net, names=T)
##       [,1]  [,2] 
##  [1,] "s01" "s02"
##  [2,] "s01" "s03"
##  [3,] "s01" "s04"
##  [4,] "s01" "s15"
##  [5,] "s02" "s01"
##  [6,] "s02" "s03"
##  [7,] "s02" "s09"
##  [8,] "s02" "s10"
##  [9,] "s03" "s01"
## [10,] "s03" "s04"
## [11,] "s03" "s05"
## [12,] "s03" "s08"
## [13,] "s03" "s10"
## [14,] "s03" "s11"
## [15,] "s03" "s12"
## [16,] "s04" "s03"
## [17,] "s04" "s06"
## [18,] "s04" "s11"
## [19,] "s04" "s12"
## [20,] "s04" "s17"
## [21,] "s05" "s01"
## [22,] "s05" "s02"
## [23,] "s05" "s09"
## [24,] "s05" "s15"
## [25,] "s06" "s06"
## [26,] "s06" "s16"
## [27,] "s06" "s17"
## [28,] "s07" "s03"
## [29,] "s07" "s08"
## [30,] "s07" "s10"
## [31,] "s07" "s14"
## [32,] "s08" "s03"
## [33,] "s08" "s07"
## [34,] "s08" "s09"
## [35,] "s09" "s10"
## [36,] "s10" "s03"
## [37,] "s12" "s06"
## [38,] "s12" "s13"
## [39,] "s12" "s14"
## [40,] "s13" "s12"
## [41,] "s13" "s17"
## [42,] "s14" "s11"
## [43,] "s14" "s13"
## [44,] "s15" "s01"
## [45,] "s15" "s04"
## [46,] "s15" "s06"
## [47,] "s16" "s06"
## [48,] "s16" "s17"
## [49,] "s17" "s04"
as_adjacency_matrix(net, attr="weight")
## 17 x 17 sparse Matrix of class "dgCMatrix"
##    [[ suppressing 17 column names 's01', 's02', 's03' ... ]]
##                                                      
## s01  . 22 22 21 .  .  .  .  .  .  .  .  .  . 20  .  .
## s02 23  . 21  . .  .  .  .  1  5  .  .  .  .  .  .  .
## s03 21  .  . 22 1  .  .  4  .  2  1  1  .  .  .  .  .
## s04  .  . 23  . .  1  .  .  .  . 22  3  .  .  .  .  2
## s05  1 21  .  . .  .  .  .  2  .  .  .  .  . 21  .  .
## s06  .  .  .  . .  1  .  .  .  .  .  .  .  .  . 21 21
## s07  .  .  1  . .  .  . 22  . 21  .  .  .  4  .  .  .
## s08  .  .  2  . .  . 21  . 23  .  .  .  .  .  .  .  .
## s09  .  .  .  . .  .  .  .  . 21  .  .  .  .  .  .  .
## s10  .  .  2  . .  .  .  .  .  .  .  .  .  .  .  .  .
## s11  .  .  .  . .  .  .  .  .  .  .  .  .  .  .  .  .
## s12  .  .  .  . .  2  .  .  .  .  .  . 22 22  .  .  .
## s13  .  .  .  . .  .  .  .  .  .  . 21  .  .  .  .  1
## s14  .  .  .  . .  .  .  .  .  .  1  . 21  .  .  .  .
## s15 22  .  .  1 .  4  .  .  .  .  .  .  .  .  .  .  .
## s16  .  .  .  . . 23  .  .  .  .  .  .  .  .  .  . 21
## s17  .  .  .  4 .  .  .  .  .  .  .  .  .  .  .  .  .
# Or data frames describing nodes and edges:
as_data_frame(net, what="edges")
from to type weight
s01 s02 hyperlink 22
s01 s03 hyperlink 22
s01 s04 hyperlink 21
s01 s15 mention 20
s02 s01 hyperlink 23
s02 s03 hyperlink 21
s02 s09 hyperlink 1
s02 s10 hyperlink 5
s03 s01 hyperlink 21
s03 s04 hyperlink 22
s03 s05 hyperlink 1
s03 s08 hyperlink 4
s03 s10 mention 2
s03 s11 hyperlink 1
s03 s12 hyperlink 1
s04 s03 hyperlink 23
s04 s06 mention 1
s04 s11 mention 22
s04 s12 hyperlink 3
s04 s17 mention 2
s05 s01 mention 1
s05 s02 hyperlink 21
s05 s09 hyperlink 2
s05 s15 mention 21
s06 s06 hyperlink 1
s06 s16 hyperlink 21
s06 s17 mention 21
s07 s03 mention 1
s07 s08 mention 22
s07 s10 hyperlink 21
s07 s14 mention 4
s08 s03 hyperlink 2
s08 s07 mention 21
s08 s09 mention 23
s09 s10 mention 21
s10 s03 hyperlink 2
s12 s06 mention 2
s12 s13 hyperlink 22
s12 s14 mention 22
s13 s12 hyperlink 21
s13 s17 mention 1
s14 s11 mention 1
s14 s13 mention 21
s15 s01 hyperlink 22
s15 s04 hyperlink 1
s15 s06 hyperlink 4
s16 s06 hyperlink 23
s16 s17 mention 21
s17 s04 hyperlink 4 
as_data_frame(net, what="vertices")
name media media.type type.label audience.size
s01 s01 NY Times 1 Newspaper 20
s02 s02 Washington Post 1 Newspaper 25
s03 s03 Wall Street Journal 1 Newspaper 30
s04 s04 USA Today 1 Newspaper 32
s05 s05 LA Times 1 Newspaper 20
s06 s06 New York Post 1 Newspaper 50
s07 s07 CNN 2 TV 56
s08 s08 MSNBC 2 TV 34
s09 s09 FOX News 2 TV 60
s10 s10 ABC 2 TV 23
s11 s11 BBC 2 TV 34
s12 s12 Yahoo News 3 Online 33
s13 s13 Google News 3 Online 23
s14 s14 Reuters.com 3 Online 12
s15 s15 NYTimes.com 3 Online 24
s16 s16 WashingtonPost.com 3 Online 28
s17 s17 AOL.com 3 Online 33

Now that we have our igraph network object, let’s make a first attempt to plot it.

plot(net) # not a pretty picture!

That doesn’t look very good. Let’s start fixing things by removing the loops in the graph.

net <- simplify(net, remove.multiple = F, remove.loops = T)

Let’s and reduce the arrow size and remove the labels (we do that by setting them to NA):

plot(net, edge.arrow.size=.4,vertex.label=NA)

1.2.1 Topological properties

degree(net)
## s01 s02 s03 s04 s05 s06 s07 s08 s09 s10 s11 s12 s13 s14 s15 s16 s17 
##   8   6  13   9   5   6   5   5   4   5   3   6   4   4   5   3   5
plot(degree_distribution(net))

hist(degree(net,mode="all"),col = "tomato")

hist(degree(net,mode="in"),col = "tomato")

hist(degree(net,mode="out"),col = "tomato")

2 Plotting networks with igraph

2.1 Plotting parameters

Plotting with igraph: the network plots have a wide set of parameters you can set. Those include node options (starting with vertex.) and edge options (starting with edge.). A list of selected options is included below, but you can also check out ?igraph.plotting for more information.

The igraph plotting parameters include (among others):

NODES
vertex.color Node color (Use colors() to determine which colors are available in R
vertex.frame.color Node border color
vertex.shape One of “none”, “circle”, “square”, “csquare”, “rectangle”, “crectangle”, “vrectangle”, “pie”, “raster”, or “sphere”
vertex.size Size of the node (default is 15)
vertex.size2 The second size of the node (e.g. for a rectangle)
vertex.label Character vector used to label the nodes
vertex.label.family Font family of the label (e.g.“Times”, “Helvetica”)
vertex.label.font Font: 1 plain, 2 bold, 3, italic, 4 bold italic, 5 symbol
vertex.label.cex Font size (multiplication factor, device-dependent)
vertex.label.dist Distance between the label and the vertex
vertex.label.degree The position of the label in relation to the vertex, where 0 is right, “pi” is left, “pi/2” is below, and “-pi/2” is above
EDGES
edge.color Edge color
edge.width Edge width, defaults to 1
edge.arrow.size Arrow size, defaults to 1
edge.arrow.width Arrow width, defaults to 1
edge.lty Line type, could be 0 or “blank”, 1 or “solid”, 2 or “dashed”, 3 or “dotted”, 4 or “dotdash”, 5 or “longdash”, 6 or “twodash”
edge.label Character vector used to label edges
edge.label.family Font family of the label (e.g.“Times”, “Helvetica”)
edge.label.font Font: 1 plain, 2 bold, 3, italic, 4 bold italic, 5 symbol
edge.label.cex Font size for edge labels
edge.curved Edge curvature, range 0-1 (FALSE sets it to 0, TRUE to 0.5)
arrow.mode Vector specifying whether edges should have arrows, possible values: 0 no arrow, 1 back, 2 forward, 3 both

OTHER

margin   Empty space margins around the plot, vector with length 4
frame    if TRUE, the plot will be framed
main     If set, adds a title to the plot
sub      If set, adds a subtitle to the plot
asp       Numeric, the aspect ratio of a plot (y/x).
palette      A color palette to use for vertex color
rescale      Whether to rescale coordinates to [-1,1]. Default is TRUE.

We can set the node & edge options in two ways - the first one is to specify them in the plot() function, as we are doing below.

# Plot with curved edges (edge.curved=.1) and reduce arrow size:
# Note that using curved edges will allow you to see multiple links
# between two nodes (e.g. links going in either direction, or multiplex links)
plot(net, edge.arrow.size=.4, edge.curved=.1)

# Set edge color to light gray, the node & border color to orange 
# Replace the vertex label with the node names stored in "media"
plot(net, edge.arrow.size=.2, edge.color="orange",
     vertex.color="orange", vertex.frame.color="#ffffff",
     vertex.label=V(net)$media, vertex.label.color="black")

The second way to set attributes is to add them to the igraph object. Let’s say we want to color our network nodes based on type of media, and size them based on degree centrality (more links -> larger node) We will also change the width of the edges based on their weight.

# Generate colors based on media type:
colrs <- c("gray50", "tomato", "gold")
V(net)$color <- colrs[V(net)$media.type]
# Compute node degrees (#links) and use that to set node size:
deg <- degree(net, mode="all")
V(net)$size <- deg*3
# We could also use the audience size value:
V(net)$size <- V(net)$audience.size*0.6

# The labels are currently node IDs.
# Setting them to NA will render no labels:
V(net)$label <- NA

# Set edge width based on weight:
E(net)$width <- E(net)$weight/6

#change arrow size and edge color:
E(net)$arrow.size <- .2
E(net)$edge.color <- "gray80"

# We can even set the network layout:
graph_attr(net, "layout") <- layout_with_lgl
plot(net)

We can also override the attributes explicitly in the plot:

plot(net, edge.color="orange", vertex.color="gray50")

It helps to add a legend explaining the meaning of the colors we used:

plot(net) 
legend(x=-1.5, y=-1.1, c("Newspaper","Television", "Online News"), pch=21,
       col="#777777", pt.bg=colrs, pt.cex=2, cex=.8, bty="n", ncol=1)

Sometimes, especially with semantic networks, we may be interested in plotting only the labels of the nodes:

plot(net, vertex.shape="none", vertex.label=V(net)$media, 
     vertex.label.font=2, vertex.label.color="gray40",
     vertex.label.cex=.7, edge.color="gray85")

Let’s color the edges of the graph based on their source node color. We can get the starting node for each edge with the ends() igraph function. It returns the start and end vertex for edges listed in the es parameter. The names parameter control whether the function returns edge names or IDs.

edge.start <- ends(net, es=E(net), names=F)[,1]
edge.col <- V(net)$color[edge.start]

plot(net, edge.color=edge.col, edge.curved=.4)

2.1.1 Exercises

  1. Calculate the degree,average degree, plot the degree distribution, obtain the adjacency matrix from the next networks
g1<-barabasi.game(100,directed = FALSE)
g2<-random.graph.game(100,0.5)
g3<-sample_smallworld(1,100,p=0.2,nei=3)
  1. Identify the vertex whose degree is the maximum
  2. Find the 10 most connected vertices.
  3. Build a network from vertex = people form this classroom, rule of connection= two people are connected if they were born in a neighbor state or in the same state. Use colors, names and sizes that reflects the totpological properties of the network.